Lesson test: Testing a hypothesis

1.[3p]
What exactly is a $p$ -value?

The probability, computed assuming $H_{0}$ , of a test statistic at least as extreme as the one observed

Correct

The probability that the null hypothesis is true

The answer is: The probability, computed assuming $H_0$, of a test statistic at least as extreme as the one observed

The probability that the result is due to chance

The answer is: The probability, computed assuming $H_0$, of a test statistic at least as extreme as the one observed

The probability that the study would replicate

The answer is: The probability, computed assuming $H_0$, of a test statistic at least as extreme as the one observed

2.[2p]
Eight cups, four with milk poured first. What is the probability of identifying all four correctly by guessing, to four decimal places?

CorrectNot quite: 0.0143

3.[3p]
With eight cups, what is the probability of getting at least three of the four right by guessing, to two decimal places?

CorrectNot quite: 0.24

4.[2p]
A sample of 25 has $\overline{x} = 12.4$ and $s = 3.0$ . What is $t$ for $H_{0} : μ = 11$ , to three decimal places?

CorrectNot quite: 2.333

5.[2p]
A result with $p = 0.30$ is evidence that the null hypothesis is true.

True

The answer is: False

False

Correct

6.[3p]
A two-sided test at level $α$ rejects $μ_{0}$ exactly when

$μ_{0}$ lies outside the $1 - α$ confidence interval, because both come from the same pivot

Correct

the sample mean lies outside the interval

The answer is: $\mu_0$ lies outside the $1-\alpha$ confidence interval, because both come from the same pivot

the $p$ -value exceeds $α$

The answer is: $\mu_0$ lies outside the $1-\alpha$ confidence interval, because both come from the same pivot

the sample size is large enough

The answer is: $\mu_0$ lies outside the $1-\alpha$ confidence interval, because both come from the same pivot

7.[3p]
Which of these are legitimate criticisms of the 0.05 threshold?

Select all that apply

It was proposed as a convenience and has no theoretical standing

Correct

It makes 0.049 and 0.051 look like different kinds of result

Correct

It says nothing about the size of the effect

Correct

It is too small to ever be reached in practice

The answer is: It was proposed as a convenience and has no theoretical standing, It makes 0.049 and 0.051 look like different kinds of result, It says nothing about the size of the effect

8.[2p]
Why must the direction of a one-sided test be fixed before seeing the data?

Choosing it afterwards halves the $p$ -value by fiat and doubles the true error rate

Correct

One-sided tests are invalid for continuous data

The answer is: Choosing it afterwards halves the $p$-value by fiat and doubles the true error rate

The alternative hypothesis must include the null value

The answer is: Choosing it afterwards halves the $p$-value by fiat and doubles the true error rate

Otherwise the test statistic cannot be computed

The answer is: Choosing it afterwards halves the $p$-value by fiat and doubles the true error rate

9.[2p]
A coin gives 60 heads in 100 tosses. The upper binomial tail is 0.0284. What is the two-sided $p$ -value, to three decimal places?

CorrectNot quite: 0.057

1.[3p] What exactly is a p-value?

2.[2p] Eight cups, four with milk poured first. What is the probability of identifying all four correctly by guessing, to four decimal places?

3.[3p] With eight cups, what is the probability of getting at least three of the four right by guessing, to two decimal places?

4.[2p] A sample of 25 has x‾=12.4 and s=3.0. What is t for H0:μ=11, to three decimal places?

5.[2p] A result with p=0.30 is evidence that the null hypothesis is true.

6.[3p] A two-sided test at level α rejects μ0 exactly when

7.[3p] Which of these are legitimate criticisms of the 0.05 threshold?

8.[2p] Why must the direction of a one-sided test be fixed before seeing the data?

9.[2p] A coin gives 60 heads in 100 tosses. The upper binomial tail is 0.0284. What is the two-sided p-value, to three decimal places?

1.[3p]
What exactly is a $p$ -value?

2.[2p]
Eight cups, four with milk poured first. What is the probability of identifying all four correctly by guessing, to four decimal places?

3.[3p]
With eight cups, what is the probability of getting at least three of the four right by guessing, to two decimal places?

4.[2p]
A sample of 25 has $\overline{x} = 12.4$ and $s = 3.0$ . What is $t$ for $H_{0} : μ = 11$ , to three decimal places?

5.[2p]
A result with $p = 0.30$ is evidence that the null hypothesis is true.

6.[3p]
A two-sided test at level $α$ rejects $μ_{0}$ exactly when

7.[3p]
Which of these are legitimate criticisms of the 0.05 threshold?

8.[2p]
Why must the direction of a one-sided test be fixed before seeing the data?

9.[2p]
A coin gives 60 heads in 100 tosses. The upper binomial tail is 0.0284. What is the two-sided $p$ -value, to three decimal places?